On 1/13/08, Hector Villafuerte <> wrote:
>
> I defined a piecewise function (specifically, a triangular wave) like this:
>
> sage: f1(x) = -abs(x) + 1
> sage: f2(x) = abs(x - 2) - 1
> sage: tri_wave = piecewise([ [(-1,1), f1], [(1,3), f2]])
>
> One can plot it and it looks very nice:
>
> sage: tri_wave.plot()
>
> But while calculating this integral I get "ValueError: Value not
> defined outside of domain."
>
> sage: integrate(tri_wave(x)^2, x, -1, 3)
>
> Is there a way to integrate piecewise-defined functions?
> As always, thanks for your help,
This is clearly broken. As a band-aide, you can at least
numerically integrate as follows:
sage: integral_numerical(lambda x: tri_wave(x)^2, -1, 3)
(1.3333333333333333, 1.4765966227514582e-14)
The first output (1.3333...) is the answer, and the second is an error bound.
-- William
